Efficient reliability-based design with second order approximations

Hu, Zhangli; Du, Xiaoping

doi:10.1080/0305215x.2018.1440292

Cited by 20 publications

(6 citation statements)

References 38 publications

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“…These generally apply optimisation search of an objective function computed based on uncertainty. Reliability based optimisation methods can also be used to solve for the most probable point solution to the robust design problem (Jiang et al 2013;Hu & Du 2019;Yin & Du 2021). Surrogate models of the mean and variance can be fit as functions of design variables (Chen et al 1996;Fang, Li, & Sudjianto 2005;Allen et al 2006;Chen, Jin, & Sudjianto 2006).…”

Section: Related Workmentioning

confidence: 99%

“…RDM is more than a statistical experiment, it involves a multiple step workflow including identifying possible sources of variability, quantifying their relative contribution with noise experiments, generating ideas for design changes that may promote variation reduction and then quantifying the ability of design changes to reduce this variability through a further set of experiments. Modern computer-based methodological updates include use of uncertainty quantification (UQ), surrogate modelling, global sensitivity analysis (GSA) and optimisation (Chen et al 1996;Du & Chen 2001;Jin, Chen, & Simpson 2001;Du, Sudjianto, & Chen 2004;Fang, Li, & Sudjianto 2005;Allen et al 2006;Chen, Jin, & Sudjianto 2006;Jiang et al 2013;Jiang, Chen, & German 2016;Hu & Du 2019;Otto & Sanchez 2019;Otto, Wang, & Uyan 2019;Nellippallil et al 2020;Sanchez, Björkman, & Otto 2020;Yin & Du 2021).…”

Section: Introductionmentioning

confidence: 99%

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Uncertainty quantification and reduction using Jacobian and Hessian information

Sánchez

Otto

2021

Des. Sci.

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Robust design methods have expanded from experimental techniques to include sampling methods, sensitivity analysis and probabilistic optimisation. Such methods typically require many evaluations. We study design and noise variable cross-term second derivatives of a response to quickly identify design variables that reduce response variability. We first compute the response uncertainty and variance decomposition to determine contributing noise variables of an initial design. Then we compute the Hessian second-derivative matrix cross-terms between the variance-contributing noise variables and proposed design change variables. Design variable with large Hessian terms are those that can reduce response variability. We relate the Hessian coefficients to reduction in Sobol indices and response variance change. Next, the first derivative Jacobian terms indicate which design variable can shift the mean to maintain a desired nominal target value. Thereby, design changes can be proposed to reduce variability while maintaining a targeted nominal value. This workflow finds changes that improve robustness with a minimal four runs per design change. We also explore further computation reductions achieved through compounding variables. An example is shown on a Stirling engine where the top four variance-contributing tolerances and design changes identified through 16 Hessian terms generated a design with 20% less variance.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Uncertainty quantification and reduction using Jacobian and Hessian information

Sánchez

Otto

2021

Des. Sci.

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“…The uncertainties are assumed to be aleatory uncertainties, which have determinate and complete uncertain information, and are represented using accurate probability density functions (PDFs). Many probabilistic uncertain analysis and optimization methodologies have been proposed to decrease the deteriorative effects of uncertainties and improve the reliability of engineering products, such as the first-order reliability design method [1][2][3], the second-order reliability design method [4][5][6], the time-dependent reliability design method [7], and the reliability-based robust design method [8].…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Representation Approach for Multiple Types of Epistemic Uncertainties Based on Cubic Normal Transformation

Peng

Gao

et al. 2020

Applied Sciences

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Many non-probabilistic approaches have been widely regarded as mathematical tools for the representation of epistemic uncertainties. However, their heavy computational burden and low computational efficiency hinder their applications in practical engineering problems. In this article, a unified probabilistic representation approach for multiple types of epistemic uncertainties is proposed based on the cubic normal transformation method. The epistemic uncertainties can be represented using an interval approach, triangular fuzzy approach, or evidence theory. The uncertain intervals of four statistical moments, which contain mean, variance, skewness, and kurtosis, are calculated using the sampling analysis method. Subsequently, the probabilistic cubic normal distribution functions are conducted for sampling points of four statistical moments of epistemic uncertainties. Finally, a calculation procedure for the construction of probabilistic representation functions is proposed, and these epistemic uncertainties are represented with belief and plausibility continuous probabilistic measure functions. Two numerical examples and one engineering example demonstrate that the proposed approach can act as an accurate probabilistic representation function with high computational efficiency.

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“…Huang et al [5] developed a new SORM with saddlepoint approximation for reliability analysis. Hu et al [6] explored a novel second order approximation for structural reliability analysis. Nakamura et al [7] discussed the Monte Carlo (MC) method by the probabilistic transient thermal analysis of an atmospheric reentry vehicle structure.…”

Section: Introductionmentioning

confidence: 99%

Weighted Regression-Based Extremum Response Surface Method for Structural Dynamic Fuzzy Reliability Analysis

Feng

Fei

2019

Energies

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The parameters considered in structural dynamic reliability analysis have strong uncertainties during machinery operation, and affect analytical precision and efficiency. To improve structural dynamic fuzzy reliability analysis, we propose the weighted regression-based extremum response surface method (WR-ERSM) based on extremum response surface method (ERSM) and weighted regression (WR), by considering the randomness of design parameters and the fuzziness of the safety criterion. Therein, we utilize the ERSM to process the transient to improve computational efficiency, by transforming the random process of structural output response into a random variable. We employ the WR to find the efficient samples with larger weights to improve the calculative accuracy. The fuzziness of the safety criterion is regarded to improve computational precision in the WR-ERSM. The WR-ERSM is applied to perform the dynamic fuzzy reliability analysis of an aeroengine turbine blisk with the fluid-structure coupling technique, and is verified by the comparison of the Monte Carlo (MC) method, equivalent stochastic transformation method (ESTM) and ERSM, with the emphasis on model-fitting property and simulation performance. As revealed from this investigation, (1) the ERSM has the capacity of processing the transient of the structural dynamic reliability evaluation, and (2) the WR approach is able to improve modeling accuracy, and (3) regarding the fuzzy safety criterion is promising to improve the precision of structural dynamic fuzzy reliability evaluation, and (4) the change rule of turbine blisk structural stress from start to cruise for the aircraft is acquired with the maximum value of structural stress at t = 165 s and the reliability degree (Pr = 0.997) of turbine blisk. The proposed WR-ERSM can improve the efficiency and precision of structural dynamic reliability analysis. Therefore, the efforts of this study provide a promising method for structural dynamic reliability evaluation with respect to working processes.

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Efficient reliability-based design with second order approximations

Cited by 20 publications

References 38 publications

Uncertainty quantification and reduction using Jacobian and Hessian information

Uncertainty quantification and reduction using Jacobian and Hessian information

Probabilistic Representation Approach for Multiple Types of Epistemic Uncertainties Based on Cubic Normal Transformation

Weighted Regression-Based Extremum Response Surface Method for Structural Dynamic Fuzzy Reliability Analysis

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